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A robophysical model of spacetime dynamics.

Shengkai Li1, Hussain N Gynai2, Steven W Tarr2

  • 1Department of Physics, Princeton University, Princeton, NJ, 08544, USA.

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Summary
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A novel robophysical analog uses a wheeled robot on a deformable membrane to precisely model dynamics in curved relativistic spacetimes. This system accurately captures how active matter moves in complex, deformable environments, offering low-cost insights into general relativity.

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Area of Science:

  • Physics
  • Robotics
  • General Relativity

Background:

  • Traditional models using rolling spheres on elastic membranes struggle to accurately represent relativistic dynamics due to dissipation and external gravity.
  • A need exists for a more accurate and controllable laboratory analog for studying general relativity and active matter dynamics.

Purpose of the Study:

  • To develop a robophysical analog that precisely captures dynamics in curved relativistic spacetimes.
  • To demonstrate how an active object, a wheeled robot, can model relativistic motion on a deformable surface.
  • To provide a low-cost laboratory system for exploring general relativity and active matter in deformable environments.

Main Methods:

  • A wheeled robot was programmed to move on a spandex membrane, altering its speed based on terrain curvature.
  • The robot's dynamics were systematically studied in radial and orbital directions to map its trajectories.
  • A framework was developed to correlate the robot's emergent motion with motion in curved spacetimes.

Main Results:

  • The active robot's dynamics were shown to exactly capture relativistic dynamics in curved spacetimes.
  • A mapping was established between the robot's trajectories on the membrane and motion in a fiducial spacetime.
  • The study demonstrated that active particles follow geodesics in a fiducial spacetime, not necessarily in real space.
  • Parameters like membrane elasticity and robot speed allow for programming specific spacetimes, such as the Schwarzschild metric.

Conclusions:

  • This robophysical analog offers a precise and cost-effective method for studying general relativity in a laboratory setting.
  • The framework provides insights into the behavior of active matter in deformable environments and robot navigation in complex landscapes.
  • The system allows for the creation and study of programmable spacetimes, enhancing our understanding of relativistic physics.